#### 2.530   ODE No. 530

$y'(x)^3-y(x) y'(x)^2+y(x)^2=0$ Mathematica : cpu = 7.8796 (sec), leaf count = 648

$\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {\#1}}\frac {\sqrt [3]{2 K[1]^3-27 K[1]^2+3 \sqrt {3} \sqrt {-K[1]^4 (4 K[1]-27)}}}{2 \sqrt [3]{2} K[1]^2+2 \sqrt [3]{2 K[1]^3-27 K[1]^2+3 \sqrt {3} \sqrt {-K[1]^4 (4 K[1]-27)}} K[1]+2^{2/3} \left (2 K[1]^3-27 K[1]^2+3 \sqrt {3} \sqrt {-K[1]^4 (4 K[1]-27)}\right )^{2/3}}dK[1]\& \right ]\left [\frac {x}{6}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {\#1}}\frac {\sqrt [3]{2 K[2]^3-27 K[2]^2+3 \sqrt {3} \sqrt {-K[2]^4 (4 K[2]-27)}}}{2 i \sqrt [3]{2} \sqrt {3} K[2]^2-2 \sqrt [3]{2} K[2]^2+4 \sqrt [3]{2 K[2]^3-27 K[2]^2+3 \sqrt {3} \sqrt {-K[2]^4 (4 K[2]-27)}} K[2]-i 2^{2/3} \sqrt {3} \left (2 K[2]^3-27 K[2]^2+3 \sqrt {3} \sqrt {-K[2]^4 (4 K[2]-27)}\right )^{2/3}-2^{2/3} \left (2 K[2]^3-27 K[2]^2+3 \sqrt {3} \sqrt {-K[2]^4 (4 K[2]-27)}\right )^{2/3}}dK[2]\& \right ]\left [\frac {x}{12}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {\#1}}\frac {\sqrt [3]{2 K[3]^3-27 K[3]^2+3 \sqrt {3} \sqrt {-K[3]^4 (4 K[3]-27)}}}{-2 i \sqrt [3]{2} \sqrt {3} K[3]^2-2 \sqrt [3]{2} K[3]^2+4 \sqrt [3]{2 K[3]^3-27 K[3]^2+3 \sqrt {3} \sqrt {-K[3]^4 (4 K[3]-27)}} K[3]+i 2^{2/3} \sqrt {3} \left (2 K[3]^3-27 K[3]^2+3 \sqrt {3} \sqrt {-K[3]^4 (4 K[3]-27)}\right )^{2/3}-2^{2/3} \left (2 K[3]^3-27 K[3]^2+3 \sqrt {3} \sqrt {-K[3]^4 (4 K[3]-27)}\right )^{2/3}}dK[3]\& \right ]\left [\frac {x}{12}+c_1\right ]\right \}\right \}$ Maple : cpu = 0.099 (sec), leaf count = 424

$\left \{ x-\int ^{y \left ( x \right ) }\!-12\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}}{4\,i{{\it \_a}}^{2}\sqrt {3}-i\sqrt {3} \left ( -108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}} \right ) ^{2/3}+4\,{{\it \_a}}^{2}-4\,{\it \_a}\,\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}+ \left ( -108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}} \right ) ^{2/3}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!6\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}}{4\,{{\it \_a}}^{2}+2\,{\it \_a}\,\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}+ \left ( -108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}} \right ) ^{2/3}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-12\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}}{i\sqrt {3} \left ( -108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}} \right ) ^{2/3}-4\,i{{\it \_a}}^{2}\sqrt {3}-4\,{\it \_a}\,\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}+ \left ( -108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}} \right ) ^{2/3}+4\,{{\it \_a}}^{2}}}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) =0 \right \}$